Polytope of Type {12,12} with group SmallGroup(864,4669)

Overview

Group: SmallGroup(864,4669)
Rank: 3
Schläfli Type: {12,12}
Vertices, edges, …: 36, 216, 36
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 12
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

4-fold

{6,12}*216c

9-fold

{4,12}*96c

12-fold

{6,4}*72

18-fold

{4,6}*48c

36-fold

{4,3}*24

Covers minimal covers in bold

2-fold

{12,12}*1728ab

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s1*s0*s2*s1*s2> of order 2

24 facets

12 of {12}*24
12 of {6}*12

18 vertex figures

18 of {12}*24

P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s1*s2*s1*s0*s2*s1> of order 3

12 facets

12 of {12}*24

12 vertex figures

12 of {12}*24

P/N, where N=<(s0*s1)^4> of order 3

24 facets

18 of {4}*8
6 of {12}*24

12 vertex figures

12 of {12}*24

Representations

Permutation Representation (GAP)

s0 := ( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,27)(14,28)(15,25)(16,26)(17,35)(18,36)(19,33)(20,34)(21,31)(22,32)(23,29)(24,30);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,17)(14,19)(15,18)(16,20)(22,23)(25,29)(26,31)(27,30)(28,32)(34,35);;
s2 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)( 9,25)(10,28)(11,27)(12,26)(18,20)(21,29)(22,32)(23,31)(24,30)(34,36);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(36)!( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,27)(14,28)(15,25)(16,26)(17,35)(18,36)(19,33)(20,34)(21,31)(22,32)(23,29)(24,30);
s1 := Sym(36)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,17)(14,19)(15,18)(16,20)(22,23)(25,29)(26,31)(27,30)(28,32)(34,35);
s2 := Sym(36)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)( 9,25)(10,28)(11,27)(12,26)(18,20)(21,29)(22,32)(23,31)(24,30)(34,36);
poly := sub<Sym(36)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.